Institute for Mathematical Physics Short{distance Analysis for Algebraic Euclidean Field Theory Short-distance Analysis for Algebraic Euclidean Eld Theory

Recently D. Buchholz and R. Verch have proposed a method for implementing in algebraic quantum eld theory ideas from renormaliza-tion group analysis of short-distance (high energy) behavior by passing to certain scaling limit theories. Buchholz and Verch distinguish between diierent types of theories where the limit is unique, degenerate, or classical, and the method allows in principle to extract thèultra-particle' content of a given model, i.e. to identify particles (like quarks and gluons) that are not visible at nite distances due tòconnnement'. It is therefore of great importance for the physical interpretation of the theory. The method has been illustrated in a simple model in with some rather surprising results. This paper will focus on the question how the short distance behavior of models deened by euclidean means is reeected in the corresponding behavior of their Minkowski counterparts. More specii-cally, we shall prove that if a euclidean theory has some short distance limit, then it is possible to pass from this limit theory to a theory on Minkowski space, which is a short distance limit of the Minkowski space theory corresponding to the original euclidean theory.